Cutting convex curves. (November 2016)

• Record Type: Journal Article
• Authors: Holmsen, Andreas F.; Kincses, János; Roldán-Pensado, Edgardo
• Is Part Of: European journal of combinatorics. Volume 58(2016:Nov.)
• Page Start: 34
• Page End: 37
• Publication Date: 2016-11
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.04.011
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We show that for any two convex curves C 1 and C 2 in R d parametrized by [ 0, 1 ] with opposite orientations, there exists a hyperplane H with the following property: For any t ∈ [ 0, 1 ] the points C 1 ( t ) and C 2 ( t ) are never in the same open half space bounded by H . This will be deduced from a more general result on equipartitions of ordered point sets by hyperplanes.